1. Field of the Invention
The present invention relates to a spectroscopic polarimetry in which, and a spectroscopic polarimeter with which, a state of spectral polarization of light under measurement is measured by the use of a channeled spectrum.
2. Description of Related Art
Light has properties of a “transverse wave”. Based upon the premise of three mutually orthogonal axes (x, y, z), when a propagation direction of light is assumed to be the z-axis direction, a vibration direction of the light is a direction along the x-y flat face. The vibration direction of the light within the x-y flat face has a bias. This bias of light is referred to as “polarization”. A biased state of light is referred to as a “state of polarization (SOP)” in this specification. Typically, the SOP varies depending upon wavelengths (colors) of light.
When light in some state of polarization is incident on an object under measurement to acquire emitted light such as transparent or reflected light and the object under measurement has optical anisotropy, a change in SOP is observed between incident light and emitting light. Acquiring information on anisotropy of the object under measurement from the change in SOP is referred to as “polarimetry”. It is to be noted that causes of such anisotropy may include anisotropy of a molecular structure, presence of stress (pressure), and presence of a local field and a magnetic field.
A measurement in which a change in SOP between the incident light and the emitted light is obtained with respect to each wavelength and information on anisotropy of an object under measurement is then acquired is especially referred to as “spectroscopic polarimetry”. This spectroscopic polarimetry has an advantage of acquiring a great amount of information as compared to the case of measurement by the use of a single wavelength (single color). In the spectroscopic polarimetry, a device for measuring an SOP of emitted light (occasionally, incident light), namely a spectroscopic polarimeter, is a key device.
As fields of application of the spectroscopic polarimetry known are the field of spectrometric ellipsometry, the medical field, the optical communication field, and the like. In the field of spectrometric ellipsometry, for example, since thickness as well as a complex refractive index of a thin film can be measured in a nondestructive and non-contact manner, spectrometric ellipsometry has been applied to optical electronic devices, analyses/examination of semiconductors, and the like. In the medical field, an attempt has been made for early detection of glaucoma or a cancer cell since several kinds of cells have polarization properties. In the optical communication field, an attempt has been made to accurately evaluate polarization mode dispersion of communication devices, such as optical fibers, for the purpose of achieving high-capacity communication by the use of wavelength division multiplexing, or some other attempts have also been made.
Incidentally, assuming that light traveling in the z-axis direction exists, polarized light in a state where a vibration component in the x-axis direction is perfectly correlated (synchronized) with a vibration component in the y-axis direction is classified into three types: linearly polarized light, elliptically polarized light, and circularly polarized light. Parameters for expressing a state of elliptically polarized light are: ε for an ellipticity angle, θ for an azimuth angle, Δ for a phase difference, and ψ for an amplitude ratio angle.
Further, parameters for effectively expressing a degree of polarization of light, the ellipticity angle, the azimuth angle and the like, Stokes Parameters are used. The Stokes Parameters are composed of four parameters having definitions as follows:
S0: total intensity
S1: difference between intensities of linear polarized components with angles of 0° and 90°.
S2: difference between intensities of linear polarized components with angles ±45°.
S3: difference between intensities of left and right circularly polarized light components.
In a third-dimensional space where the three mutually orthogonal axes are taken as S1, S2 and S3, assuming a sphere with a radius S0 and an original point of the axes taken as a center, an SOP of arbitrary light is expressed as one point in this third-dimensional space and a degree of polarization is expressed by the following expression:
                              Degree          ⁢                                          ⁢          of          ⁢                                          ⁢          polarization                =                ⁢                  (                      distance            ⁢                                                  ⁢            from            ⁢                                                                      ⁢                                                                    ⁢            original            ⁢                                                  ⁢            point            ⁢                                                  ⁢            to                                                          ⁢                  point          ⁢                                          ⁢                                    (                                                S                  1                                ,                                  S                  2                                ,                                  S                  3                                            )                        /                          S              0                                                              =                ⁢                                            (                                                S                  1                  2                                +                                  S                  2                  2                                +                                  S                  3                  2                                            )                                      1              /              2                                /                      S            0                              
It may be understood from the above that in the case of a perfectly polarized light (degree of polarization=1), one point expressing the SOP exists in the sphere with a radius S0. Further, the ellipticity angle and the azimuth angle respectively correspond to halves of a latitude and a longitude of the one point expressing the SOP in the above third-dimensional space. As thus described, it is possible to express all information on the SOP if the four parameters S1, S2, S3 and S0 of the Stokes Parameters can be obtained.
As conventionally prevailing spectroscopic polarimetries, a rotating-retarder polarimetry and a polarization-modulation polarimetry are known.
In the rotating-retarder polarimetry, a retarder and an analyzer intervene in sequence in a channel for light under measurement toward a spectrometer. Here, the retarder is an optical element having two principal axes (fast axis and slow axis) in mutually orthogonal directions, and is also configured to change a phase difference between the two principal axes before and after passage of light. Further, the analyzer is an optical element having one principal axis and also is configured to allow transmission of only one linearly polarized light component corresponding to the direction of the principal axis.
In this rotating-retarder polarimetry, for obtaining wavelength distributions of the four Stokes Parameters independently, it is necessary to physically rotate a retarder itself and perform a spectrum measurement each for at least four kinds of directions. Namely, the Stokes Parameters of incident light are expressed as functions S0(λ), S1(λ), S2(λ), and S3(λ).
In the polarization-modulation polarimetry, two retarders (first retarder and second retarder) capable of electrically controlling a phase difference and one analyzer intervene in sequence in a channel for light under measurement toward a spectrometer. Among such retarders used are an electro-optic modulator, a liquid crystal and a photoelastic modulator. For example, a phase difference of 45° is set between the principal axes of the first retarder and the second retarder.
Also in this polarization-modulation polarimetry, for obtaining wavelength distributions of the four Stokes Parameters independently, it is necessary to vibrate, by electric control, a phase difference between the first retarder and the second retarder in a predetermined angle range to obtain a plurality of spectrums.
However, concerning the conventional general spectroscopic polarimetry typified by the rotating-retarder polarimetry and the polarization-modulation polarimetry, the following problems have been pointed out.
(1) First Problem
Since a mechanical or active polarization controlling element is required, there are problems including that: [1] a problem of vibration, heat generation and the like are unavoidable; [2] the degree of size reduction is limited due to necessity for a mechanical element and the like to have some capacity; [3] a driving device for consuming electric power is essential; and [4] maintenance is necessary and complex.
(2) Second Problem
Since it is necessary to repeatedly measure a plurality of spectrums while changing conditions of the polarization modulating (controlling) element, there are problems including that: [1] measurement takes relatively long; and [2] an object under measurement needs to be kept stable during measurement.
In order to solve the above problems with the conventional general spectroscopic polarimetry, the present inventors and the like developed, in advance, a “channeled spectroscopic polarimetry”.
A configuration view of an experiment system for explaining the channeled spectroscopic polarimetry is shown in FIG. 20. As apparent from this figure, white light emitted from a xenon lamp 1 is transmitted through a polarizer 2 and a Babinet-Soleil compensator 3, to obtain a light wave having an SOP depending upon a frequency ν. Spectral distributions S0(ν), S1(ν), S2(ν) and S3(ν) of the Stokes parameters of the light wave are obtained by a measurement system 4 surrounded with a wavy line.
Light under measurement is first transmitted through two retarders R1 and R2 having different thicknesses (d1, d2) and an analyzer A, and then incident on a spectrometer 5. Here, the slow axis of the retarder R2 is inclined at an angle of 45° with respect to the slow axis of the retarder R1, while a transmission axis of the analyzer A is arranged in parallel to the slow axis of the retarder R1.
In each of the two retarders R1 and R2, a phase difference created between the orthogonal polarized light components depends upon a frequency. Hence, as shown in FIG. 21, a channeled spectrum including three carrier components is obtained from the spectrometer 5 which functions as an optical spectrum analyzer. An amplitude and a phase of each of the carrier components are modulated by the spectrum distribution of the Stokes Parameters of the light under measurement. It is therefore possible to obtain each of the Stokes Parameters by execution of a signal processing with a computer 6 by the use of Fourier transformation.
One example of results of an experiment is shown in FIG. 22. This is a result obtained in the case of inclining the Babinet-Soleil compensator 3 at an angle of 30° with respect to the slow axis of the retarder R1. Three solid lines respectively show spectral distributions S1(ν)/S0(ν), S2(ν)/S0(ν), S3(ν)/S0(ν) of the standardized Stokes parameters. It is thereby understood that an SOP depends upon a frequency.
As thus described, according to the channeled spectroscopic polarimetry, it is possible to obtain each spectrally-resolved Stokes Parameter by a frequency analysis (or wavenumber analysis) of properties of spectral intensity. It is reasonably necessary to obtain respective retardations of the two retarders S1 and S2 prior to the frequency analysis. Here, retardation means a phase difference created between a fast axis component and a slow axis component.
Other conventional channeled spectroscopic polarimetries are described in some other documents (cf. Patent Document 1 and Non-patent Document 1).
According to the foregoing channeled spectroscopic polarimetry, advantages can be obtained including that: [1] a mechanically movable element such as a rotating retarder is unnecessary; [2] an active element such as an electro-optic modulator is unnecessary; [3] four Stokes Parameters stop all at once with one spectrum so that a so-called snap shot measurement can be performed; and [4] the configuration is simple, and thus suitable for size reduction.
[Patent Document 1] U.S. Pat. No. 6,490,043
[Non-patent Document 1] “Measurement of spectral distribution of polarized light based on frequency region interference method”, written by Takayuki Kato, Kazuhiko Oka, Tetsu Tanaka, Yoshihiro Ohtsuka, preliminary manuscript collection for 34th Academic Lecture Meeting of Hokkaido Branch of Japan Society of Applied Physics, (Hokkaido Branch of Japan Society of Applied Physics, Sapporo, 1998) p. 41
However, concerning the foregoing channeled spectroscopic polarimetry, a problem of generation of a relatively large measurement error has been pointed out for the following reasons.
(1) Variations (Fluctuations) in Retardation of retarders R1, R2 
Retardation of the retarder varies sensitively due to a temperature or pressure change, resulting in that the phase of the channeled spectrum varies due to the temperature or pressure change, as shown in FIG. 23. Consequently, as shown in FIG. 24, the temperature or pressure change causes generation of an error in a measured value of the Stokes parameter obtained from the channeled spectrum.
(2) Variations (Fluctuations) in Wavelength Axis of Spectrometer
In a normal type spectrometer such as one that rotates a diffraction grating with a motor, backlash of the motor or the like causes displacement of a wavelength to be sampled by small degree (at random) in every measurement. When the wavelength to be sampled is displaced in the spectrometer as shown in FIG. 25, a state is generated which is equivalent to a case where retardation of a retarder varies, resulting in generation of an error in a measured value of the Stokes parameter obtained from the channeled spectrum.
Incidentally, for example in ellipsometry, accuracy required in a wavenumber-distribution of an ellipsometry parameter is considered to be an error in the order of not larger than 0.1°. When this accuracy is to be realized by stabilizing retardation of a retarder, it is necessary to keep variations in temperature of the retarder at or under 0.5° C.
However, it requires a large-sized temperature compensating device such as a heater or a cooler for the temperature stabilization, which unfavorably causes a loss of advantages (size reduction, non-inclusion of an active element, etc.) of the channeled spectroscopic polarimetry. Hence it is practically difficult to reduce a measurement error by stabilizing retardation of a retarder.
Further, reduction of backlash of the spectrometer to a satisfactory value requires extremely high process accuracy or assembly accuracy, thereby leading to an expensive spectrometer. Hence it is practically difficult to reduce a measurement error by stabilizing a wavelength axis of a spectrometer.